4x^2+5=6x-x^2+10

Solution for 4x^2+5=6x-x^2+10 equation:

4x^2+5=6x-x^2+10

We move all terms to the left:

4x^2+5-(6x-x^2+10)=0

We get rid of parentheses

4x^2+x^2-6x-10+5=0

We add all the numbers together, and all the variables

5x^2-6x-5=0

a = 5; b = -6; c = -5;
Δ = b2-4ac
Δ = -62-4·5·(-5)
Δ = 136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{34}}{2*5}=\frac{6-2\sqrt{34}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{34}}{2*5}=\frac{6+2\sqrt{34}}{10}
$